Adaptive multiple subtraction with a non-stationary regularization factor

Adaptive multiple subtraction is essential for the success of surface-related multiple elimination. For balancing multiple removal and primary preservation, a robust adaptive multiple subtraction can be employed, which uses an L1 norm minimization constraint on the primaries to estimate the matching filter. Additionally, an energy minimization constraint of the filter coefficients is used to ensure the stability of the filter estimation and to avoid primary distortion caused by large filter coefficients. The regularization factor balances the contributions from primaries and filter coefficients. The traditional stationary robust adaptive multiple subtraction assigns the same regularization factors in different data windows. Since the stationary robust method does not consider the non-stationary characteristics of primaries, it can not balance multiple removal and primary preservation effectively. To solve this problem, I propose a non-stationary robust adaptive multiple subtraction process, which determines the regularization factor as a function of the energy ratio between primaries and the original data. The non-stationary regularization factor assigns different values in different data windows by using the non-stationary characteristics of primaries. Compared to the traditional stationary robust subtraction method and the widely used least-squares subtraction method, the proposed method can remove more residual multiples while preserving primaries effectively. Synthetic and field data examples demonstrate the effectiveness of the proposed method.